K Schur Functions And Affine Schubert Calculus

Download K Schur Functions And Affine Schubert Calculus full books in PDF, epub, and Kindle. Read online K Schur Functions And Affine Schubert Calculus ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!

k-Schur Functions and Affine Schubert Calculus

Author : Thomas Lam
Publisher : Springer
ISBN 13 : 1493906828
Total Pages : 226 pages
Book Rating : 4.4/5 (939 download)

DOWNLOAD NOW!

Book Synopsis k-Schur Functions and Affine Schubert Calculus by : Thomas Lam

Download or read book k-Schur Functions and Affine Schubert Calculus written by Thomas Lam and published by Springer. This book was released on 2014-06-05 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an introduction to the very active field of combinatorics of affine Schubert calculus, explains the current state of the art, and states the current open problems. Affine Schubert calculus lies at the crossroads of combinatorics, geometry, and representation theory. Its modern development is motivated by two seemingly unrelated directions. One is the introduction of k-Schur functions in the study of Macdonald polynomial positivity, a mostly combinatorial branch of symmetric function theory. The other direction is the study of the Schubert bases of the (co)homology of the affine Grassmannian, an algebro-topological formulation of a problem in enumerative geometry. This is the first introductory text on this subject. It contains many examples in Sage, a free open source general purpose mathematical software system, to entice the reader to investigate the open problems. This book is written for advanced undergraduate and graduate students, as well as researchers, who want to become familiar with this fascinating new field.

K-Schur Functions and Affine Schubert Calculus

Author : Thomas Lam
Publisher :
ISBN 13 : 9781493906833
Total Pages : 228 pages
Book Rating : 4.9/5 (68 download)

DOWNLOAD NOW!

Book Synopsis K-Schur Functions and Affine Schubert Calculus by : Thomas Lam

Download or read book K-Schur Functions and Affine Schubert Calculus written by Thomas Lam and published by . This book was released on 2014-06-30 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Poset of $k$-Shapes and Branching Rules for $k$-Schur Functions

Author : Thomas Lam
Publisher : American Mathematical Soc.
ISBN 13 : 082187294X
Total Pages : 101 pages
Book Rating : 4.8/5 (218 download)

DOWNLOAD NOW!

Book Synopsis The Poset of $k$-Shapes and Branching Rules for $k$-Schur Functions by : Thomas Lam

Download or read book The Poset of $k$-Shapes and Branching Rules for $k$-Schur Functions written by Thomas Lam and published by American Mathematical Soc.. This book was released on 2013-04-22 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors give a combinatorial expansion of a Schubert homology class in the affine Grassmannian $\mathrm{Gr}_{\mathrm{SL}_k}$ into Schubert homology classes in $\mathrm{Gr}_{\mathrm{SL}_{k+1}}$. This is achieved by studying the combinatorics of a new class of partitions called $k$-shapes, which interpolates between $k$-cores and $k+1$-cores. The authors define a symmetric function for each $k$-shape, and show that they expand positively in terms of dual $k$-Schur functions. They obtain an explicit combinatorial description of the expansion of an ungraded $k$-Schur function into $k+1$-Schur functions. As a corollary, they give a formula for the Schur expansion of an ungraded $k$-Schur function.

Affine Insertion and Pieri Rules for the Affine Grassmannian

Author : Thomas Lam
Publisher : American Mathematical Soc.
ISBN 13 : 0821846582
Total Pages : 82 pages
Book Rating : 4.8/5 (218 download)

DOWNLOAD NOW!

Book Synopsis Affine Insertion and Pieri Rules for the Affine Grassmannian by : Thomas Lam

Download or read book Affine Insertion and Pieri Rules for the Affine Grassmannian written by Thomas Lam and published by American Mathematical Soc.. This book was released on 2010 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study combinatorial aspects of the Schubert calculus of the affine Grassmannian ${\rm Gr}$ associated with $SL(n,\mathbb{C})$.Their main results are: Pieri rules for the Schubert bases of $H^*({\rm Gr})$ and $H_*({\rm Gr})$, which expresses the product of a special Schubert class and an arbitrary Schubert class in terms of Schubert classes. A new combinatorial definition for $k$-Schur functions, which represent the Schubert basis of $H_*({\rm Gr})$. A combinatorial interpretation of the pairing $H^*({\rm Gr})\times H_*({\rm Gr}) \rightarrow\mathbb Z$ induced by the cap product.

Schubert Calculus and Its Applications in Combinatorics and Representation Theory

Author : Jianxun Hu
Publisher : Springer Nature
ISBN 13 : 9811574510
Total Pages : 367 pages
Book Rating : 4.8/5 (115 download)

DOWNLOAD NOW!

Book Synopsis Schubert Calculus and Its Applications in Combinatorics and Representation Theory by : Jianxun Hu

Download or read book Schubert Calculus and Its Applications in Combinatorics and Representation Theory written by Jianxun Hu and published by Springer Nature. This book was released on 2020-10-24 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers research papers and surveys on the latest advances in Schubert Calculus, presented at the International Festival in Schubert Calculus, held in Guangzhou, China on November 6–10, 2017. With roots in enumerative geometry and Hilbert's 15th problem, modern Schubert Calculus studies classical and quantum intersection rings on spaces with symmetries, such as flag manifolds. The presence of symmetries leads to particularly rich structures, and it connects Schubert Calculus to many branches of mathematics, including algebraic geometry, combinatorics, representation theory, and theoretical physics. For instance, the study of the quantum cohomology ring of a Grassmann manifold combines all these areas in an organic way. The book is useful for researchers and graduate students interested in Schubert Calculus, and more generally in the study of flag manifolds in relation to algebraic geometry, combinatorics, representation theory and mathematical physics.

Affine Insertion and Pieri Rules for the Affine Grassmannian

Author : Thomas Lam
Publisher :
ISBN 13 : 9781470405915
Total Pages : 82 pages
Book Rating : 4.4/5 (59 download)

DOWNLOAD NOW!

Book Synopsis Affine Insertion and Pieri Rules for the Affine Grassmannian by : Thomas Lam

Download or read book Affine Insertion and Pieri Rules for the Affine Grassmannian written by Thomas Lam and published by . This book was released on 2010 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Facets of Algebraic Geometry

Author : Paolo Aluffi
Publisher : Cambridge University Press
ISBN 13 : 1108792510
Total Pages : 395 pages
Book Rating : 4.1/5 (87 download)

DOWNLOAD NOW!

Book Synopsis Facets of Algebraic Geometry by : Paolo Aluffi

Download or read book Facets of Algebraic Geometry written by Paolo Aluffi and published by Cambridge University Press. This book was released on 2022-04-07 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written to honor the enduring influence of William Fulton, these articles present substantial contributions to algebraic geometry.

Recent Trends in Algebraic Combinatorics

Author : Hélène Barcelo
Publisher : Springer
ISBN 13 : 3030051412
Total Pages : 362 pages
Book Rating : 4.0/5 (3 download)

DOWNLOAD NOW!

Book Synopsis Recent Trends in Algebraic Combinatorics by : Hélène Barcelo

Download or read book Recent Trends in Algebraic Combinatorics written by Hélène Barcelo and published by Springer. This book was released on 2019-01-21 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume features a curated selection of research in algebraic combinatorics that explores the boundaries of current knowledge in the field. Focusing on topics experiencing broad interest and rapid growth, invited contributors offer survey articles on representation theory, symmetric functions, invariant theory, and the combinatorics of Young tableaux. The volume also addresses subjects at the intersection of algebra, combinatorics, and geometry, including the study of polytopes, lattice points, hyperplane arrangements, crystal graphs, and Grassmannians. All surveys are written at an introductory level that emphasizes recent developments and open problems. An interactive tutorial on Schubert Calculus emphasizes the geometric and topological aspects of the topic and is suitable for combinatorialists as well as geometrically minded researchers seeking to gain familiarity with relevant combinatorial tools. Featured authors include prominent women in the field known for their exceptional writing of deep mathematics in an accessible manner. Each article in this volume was reviewed independently by two referees. The volume is suitable for graduate students and researchers interested in algebraic combinatorics.

The Mathematical Legacy of Richard P. Stanley

Author : Patricia Hersh
Publisher : American Mathematical Soc.
ISBN 13 : 1470427249
Total Pages : 352 pages
Book Rating : 4.4/5 (74 download)

DOWNLOAD NOW!

Book Synopsis The Mathematical Legacy of Richard P. Stanley by : Patricia Hersh

Download or read book The Mathematical Legacy of Richard P. Stanley written by Patricia Hersh and published by American Mathematical Soc.. This book was released on 2016-12-08 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Richard Stanley's work in combinatorics revolutionized and reshaped the subject. His lectures, papers, and books inspired a generation of researchers. In this volume, these researchers explain how Stanley's vision and insights influenced and guided their own perspectives on the subject. As a valuable bonus, this book contains a collection of Stanley's short comments on each of his papers. This book may serve as an introduction to several different threads of ongoing research in combinatorics as well as giving historical perspective.

Enumerative Combinatorics: Volume 2

Author : Richard Stanley
Publisher : Cambridge University Press
ISBN 13 : 1009262513
Total Pages : 802 pages
Book Rating : 4.0/5 (92 download)

DOWNLOAD NOW!

Book Synopsis Enumerative Combinatorics: Volume 2 by : Richard Stanley

Download or read book Enumerative Combinatorics: Volume 2 written by Richard Stanley and published by Cambridge University Press. This book was released on 2023-07-31 with total page 802 pages. Available in PDF, EPUB and Kindle. Book excerpt: Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of volume two covers the composition of generating functions, in particular the exponential formula and the Lagrange inversion formula, labelled and unlabelled trees, algebraic, D-finite, and noncommutative generating functions, and symmetric functions. The chapter on symmetric functions provides the only available treatment of this subject suitable for an introductory graduate course and focusing on combinatorics, especially the Robinson–Schensted–Knuth algorithm. An appendix by Sergey Fomin covers some deeper aspects of symmetric functions, including jeu de taquin and the Littlewood–Richardson rule. The exercises in the book play a vital role in developing the material, and this second edition features over 400 exercises, including 159 new exercises on symmetric functions, all with solutions or references to solutions.

Lie Groups, Geometry, and Representation Theory

Author : Victor G. Kac
Publisher : Springer
ISBN 13 : 3030021912
Total Pages : 540 pages
Book Rating : 4.0/5 (3 download)

DOWNLOAD NOW!

Book Synopsis Lie Groups, Geometry, and Representation Theory by : Victor G. Kac

Download or read book Lie Groups, Geometry, and Representation Theory written by Victor G. Kac and published by Springer. This book was released on 2018-12-12 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, dedicated to the memory of the great American mathematician Bertram Kostant (May 24, 1928 – February 2, 2017), is a collection of 19 invited papers by leading mathematicians working in Lie theory, representation theory, algebra, geometry, and mathematical physics. Kostant’s fundamental work in all of these areas has provided deep new insights and connections, and has created new fields of research. This volume features the only published articles of important recent results of the contributors with full details of their proofs. Key topics include: Poisson structures and potentials (A. Alekseev, A. Berenstein, B. Hoffman) Vertex algebras (T. Arakawa, K. Kawasetsu) Modular irreducible representations of semisimple Lie algebras (R. Bezrukavnikov, I. Losev) Asymptotic Hecke algebras (A. Braverman, D. Kazhdan) Tensor categories and quantum groups (A. Davydov, P. Etingof, D. Nikshych) Nil-Hecke algebras and Whittaker D-modules (V. Ginzburg) Toeplitz operators (V. Guillemin, A. Uribe, Z. Wang) Kashiwara crystals (A. Joseph) Characters of highest weight modules (V. Kac, M. Wakimoto) Alcove polytopes (T. Lam, A. Postnikov) Representation theory of quantized Gieseker varieties (I. Losev) Generalized Bruhat cells and integrable systems (J.-H. Liu, Y. Mi) Almost characters (G. Lusztig) Verlinde formulas (E. Meinrenken) Dirac operator and equivariant index (P.-É. Paradan, M. Vergne) Modality of representations and geometry of θ-groups (V. L. Popov) Distributions on homogeneous spaces (N. Ressayre) Reduction of orthogonal representations (J.-P. Serre)

Issues in General and Specialized Mathematics Research: 2011 Edition

Author :
Publisher : ScholarlyEditions
ISBN 13 : 1464964939
Total Pages : 864 pages
Book Rating : 4.4/5 (649 download)

DOWNLOAD NOW!

Book Synopsis Issues in General and Specialized Mathematics Research: 2011 Edition by :

Download or read book Issues in General and Specialized Mathematics Research: 2011 Edition written by and published by ScholarlyEditions. This book was released on 2012-01-09 with total page 864 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in General and Specialized Mathematics Research: 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about General and Specialized Mathematics Research. The editors have built Issues in General and Specialized Mathematics Research: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about General and Specialized Mathematics Research in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in General and Specialized Mathematics Research: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Affine Insertion and Pieri Rules for the Affine Grassmannian

Author :
Publisher : American Mathematical Soc.
ISBN 13 : 0821867180
Total Pages : 103 pages
Book Rating : 4.8/5 (218 download)

DOWNLOAD NOW!

Book Synopsis Affine Insertion and Pieri Rules for the Affine Grassmannian by :

Download or read book Affine Insertion and Pieri Rules for the Affine Grassmannian written by and published by American Mathematical Soc.. This book was released on with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Volume 208, number 977 (second of 6 numbers)."

Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics

Author : Mahir Can
Publisher : Springer
ISBN 13 : 149390938X
Total Pages : 360 pages
Book Rating : 4.4/5 (939 download)

DOWNLOAD NOW!

Book Synopsis Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics by : Mahir Can

Download or read book Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics written by Mahir Can and published by Springer. This book was released on 2014-06-11 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a collection of fifteen articles and is dedicated to the sixtieth birthdays of Lex Renner and Mohan Putcha, the pioneers of the field of algebraic monoids. Topics presented include: structure and representation theory of reductive algebraic monoids monoid schemes and applications of monoids monoids related to Lie theory equivariant embeddings of algebraic groups constructions and properties of monoids from algebraic combinatorics endomorphism monoids induced from vector bundles Hodge–Newton decompositions of reductive monoids A portion of these articles are designed to serve as a self-contained introduction to these topics, while the remaining contributions are research articles containing previously unpublished results, which are sure to become very influential for future work. Among these, for example, the important recent work of Michel Brion and Lex Renner showing that the algebraic semi groups are strongly π-regular. Graduate students as well as researchers working in the fields of algebraic (semi)group theory, algebraic combinatorics and the theory of algebraic group embeddings will benefit from this unique and broad compilation of some fundamental results in (semi)group theory, algebraic group embeddings and algebraic combinatorics merged under the umbrella of algebraic monoids.

Singularities and Their Interaction with Geometry and Low Dimensional Topology

Author : Javier Fernández de Bobadilla
Publisher : Springer Nature
ISBN 13 : 3030619583
Total Pages : 332 pages
Book Rating : 4.0/5 (36 download)

DOWNLOAD NOW!

Book Synopsis Singularities and Their Interaction with Geometry and Low Dimensional Topology by : Javier Fernández de Bobadilla

Download or read book Singularities and Their Interaction with Geometry and Low Dimensional Topology written by Javier Fernández de Bobadilla and published by Springer Nature. This book was released on 2021-05-27 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a collection of surveys and original research articles concentrating on new perspectives and research directions at the crossroads of algebraic geometry, topology, and singularity theory. The papers, written by leading researchers working on various topics of the above fields, are the outcome of the “Némethi60: Geometry and Topology of Singularities” conference held at the Alfréd Rényi Institute of Mathematics in Budapest, from May 27 to 31, 2019. Both the conference and this resulting volume are in honor of Professor András Némethi, on the occasion of his 60th birthday, whose work plays a decisive and influential role in the interactions between the above fields. The book should serve as a valuable resource for graduate students and researchers to deepen the new perspectives, methods, and connections between geometry and topology regarding singularities.

Crystal Bases: Representations And Combinatorics

Author : Daniel Bump
Publisher : World Scientific Publishing Company
ISBN 13 : 9814733466
Total Pages : 292 pages
Book Rating : 4.8/5 (147 download)

DOWNLOAD NOW!

Book Synopsis Crystal Bases: Representations And Combinatorics by : Daniel Bump

Download or read book Crystal Bases: Representations And Combinatorics written by Daniel Bump and published by World Scientific Publishing Company. This book was released on 2017-01-17 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book provides the first introduction to crystal base theory from the combinatorial point of view. Crystal base theory was developed by Kashiwara and Lusztig from the perspective of quantum groups. Its power comes from the fact that it addresses many questions in representation theory and mathematical physics by combinatorial means. This book approaches the subject directly from combinatorics, building crystals through local axioms (based on ideas by Stembridge) and virtual crystals. It also emphasizes parallels between the representation theory of the symmetric and general linear groups and phenomena in combinatorics. The combinatorial approach is linked to representation theory through the analysis of Demazure crystals. The relationship of crystals to tropical geometry is also explained.

Polynomial Rings and Affine Algebraic Geometry

Author : Shigeru Kuroda
Publisher : Springer Nature
ISBN 13 : 3030421368
Total Pages : 317 pages
Book Rating : 4.0/5 (34 download)

DOWNLOAD NOW!

Book Synopsis Polynomial Rings and Affine Algebraic Geometry by : Shigeru Kuroda

Download or read book Polynomial Rings and Affine Algebraic Geometry written by Shigeru Kuroda and published by Springer Nature. This book was released on 2020-03-27 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume gathers selected, peer-reviewed works presented at the Polynomial Rings and Affine Algebraic Geometry Conference, which was held at Tokyo Metropolitan University on February 12-16, 2018. Readers will find some of the latest research conducted by an international group of experts on affine and projective algebraic geometry. The topics covered include group actions and linearization, automorphism groups and their structure as infinite-dimensional varieties, invariant theory, the Cancellation Problem, the Embedding Problem, Mathieu spaces and the Jacobian Conjecture, the Dolgachev-Weisfeiler Conjecture, classification of curves and surfaces, real forms of complex varieties, and questions of rationality, unirationality, and birationality. These papers will be of interest to all researchers and graduate students working in the fields of affine and projective algebraic geometry, as well as on certain aspects of commutative algebra, Lie theory, symplectic geometry and Stein manifolds.